Somebody else here might have a better answer than me.

I think you will have to stay with 6 gears, unless you change to a different (wider) hub that will accept 7 or 8 gears. And then you'll probably have to cold set your dropouts to a wider spacing to take the wider hub (not hard to do.).

That's assuming you have a narrow-spaced six speed (i.e., one that is the same width as a five speed, but with six gears.). On the other hand, if you have a wide-spaced six speed, I think you will be able to fit a narrow-spaced seven speed cassette in there without making any other changes (except when you change from a wide-spaced to a narrow-spaced cassette, you have to change to a narrow chain.).

You'd have to get a bike mechanic to tell you if it's narrow or wide-spaced, unless you have a set of calipers and can measure your hubs...